Editorial: Forward and Inverse Solvers in Multi-Modal Electric and Magnetic Brain Imaging: Theory, Implementation, and Application

Takfarinas MEDANI^1*Sampsa Pursiainen²Maria-Carla Piastra³Johannes Vorwerk⁴Richard Leahy¹

• ¹University of Southern California, Los Angeles, United States
• ²Tampere University, Tempere, Finland
• ³University of Twente, Enschede, Netherlands
• ⁴University of Innsbruck, Innsbruck, Austria

Understanding the complexities of brain function and structure remains one of the most challenging and exciting frontiers in neuroscience [1]. Advances in multi-modal brain imaging, integrating electrophysiological and magnetophysiological techniques such as non-invasive electroencephalography (EEG), invasive electroencephalography (iEEG), including both stereo-electroencephalography (sEEG), electrocorticography (ECoG), and magnetoencephalography (MEG), have provided unprecedented insights into neural dynamics [2][3][4]. A central challenge in this domain is solving the forward and inverse problems, which enable the estimation of the brain activity underlying measured signals [4][5][6][7][8][9][10].This Research Topic aimed to bring together cutting-edge research on the theoretical foundations, computational methodologies, and practical applications of forward and inverse solvers in multi-modal electric and magnetic brain imaging. The contributions within this collection span fundamental methodological advances, novel algorithmic frameworks, and state-of-the-art applications that push the boundaries of neuroimaging.One of the significant challenges in EEG/MEG source analysis is accounting for the uncertainties in tissue conductivity. Vorwerk et al. investigated the global sensitivity of EEG source analysis to tissue conductivity uncertainties, emphasizing the importance of accurate head volume conductor models in forward problem solutions [11][12][13]. Their findings highlight how variations in tissue conductivity can significantly impact source localization accuracy, concluding that an accurate parametrization of the head volume conductor model is as important as an accurate representation of the geometry [7,11,12]. Piastra et al. conducted a validation study using stereotactic sEEG data to assess the accuracy of head volume conductor models. Their work underscores the necessity of precise modeling in achieving reliable source localization in combination with empirical validations. Erdbrügger et al. introduced the CutFEM forward modeling approach for EEG source analysis [14][15][16][17]. This method offers enhanced flexibility in handling complex geometries and tissue interfaces in head volume conductor models, contributing to more accurate forward solutions in EEG studies.Advancements in algorithmic frameworks are crucial for improving source localization techniques. Luria et al. presented the SESAMEEG package, a probabilistic tool for source localization and uncertainty quantification in MEG/EEG analysis [18][19][20]. This package facilitates more robust and interpretable source estimates by incorporating probabilistic modeling. Ghosh et al. developed the Structured Noise Champagne algorithm, an empirical Bayesian approach for electromagnetic brain imaging that accounts for structured noise. This method enhances the reliability of source reconstructions in the presence of complex noise structures [4,6]. Giri et al. proposed an F-ratio-based method for estimating the number of active sources in MEG data. Their approach aids in determining the optimal model complexity, balancing the trade-off between model fit and overfitting [21].The practical impact of these methodological advancements has been demonstrated in numerous studies. Guillen et al. explored optimized high-definition transcranial direct current stimulation (tDCS) in patients with skull defects and implants, demonstrating the clinical relevance of accurate modeling in neuromodulation therapies [22][23][24][25]. Huang et al. visualized interferential stimulation of human brains, providing insights into the spatial distribution of electric fields during stimulation protocols [26,27]. This work contributes to the optimization of stimulation parameters for therapeutic interventions. Furthermore, Galaz Prieto et al. analyzed the effects of lattice layout and optimizer selection on generating optimal transcranial electrical stimulation (tES) montages using the metaheuristic L1L1 method. Their findings inform the design of more effective stimulation configurations.Collectively, these contributions underscore the importance of integrating theoretical, computational, and practical perspectives in advancing EEG/MEG source analysis as well as tES modeling. Future research directions may include the development of standardized pipelines [11,23,[28][29][30], the incorporation of machine learning techniques for model selection and parameter estimation, and the expansion of open-source tools to facilitate broader accessibility and reproducibility in the field [30][31][32][33][34][35][36][37][38].